Gauge Theory Of Gravity Research Articles

Accelerating Universe with spacetime torsion but without dark matter and dark energy

It is shown that cosmological equations for homogeneous isotropic models deduced in the framework of the Poincaré gauge theory of gravity by certain restrictions on indefinite parameters of gravitational Lagrangian take at asymptotics the same form as cosmological equations of general relativity theory for ΛCDM-model. Terms related to dark matter and dark energy in cosmological equations of standard theory for ΛCDM-model are connected in considered theory with the change of gravitational interaction provoked by spacetime torsion.

Modified coupling procedure for the Poincaré gauge theory of gravity

The minimal coupling procedure, which is employed in standard Yang-Mills theories, appears to be ambiguous in the case of gravity. We propose a slight modification of this procedure, which removes the ambiguity. Our modification justifies some earlier results concerning the consequences of the Poincar\'e gauge theory of gravity. In particular, the predictions of the Einstein-Cartan theory with fermionic matter are rendered unique.

Local Poincaré Symmetry in Gauge Theory of Gravity

It is well known that the Poincaré gauge theories of gravity do not have the structure of a standard gauge theory. Nevertheless, we show that a general form of action for the gravitational gauge fields in the gauge theory does possess local Poincaré invariance.

A gravitational constant and a cosmological constant in a spin-connection gravitational gauge field theory

A spin-connection gravitational gauge theory with a spin-affine connection as its fundamental dynamical variable is suggested in the framework of vierbein formulation. The functional integral approach to the interaction between complex scalar matter fields and a heavy intermediate coupling field is considered, where the Einstein field equation appears as a first-integral solution to the low-energy spin-connection gauge field equation of Yang–Mills type. The most intriguing characteristics of the present scheme include: (i) the gravitational constant originates from the low-energy propagator of the heavy coupling field that mediates the gravitation between the matter fields and the spin-connection gauge field; (ii) the large cosmological constant resulting from the quantum vacuum energy actually makes no gravitational contribution since the spin-connection gauge field equation is a third-order differential equation of the metric, and an integration constant of the first-integral solution serves as an effective cosmological constant that would cause the cosmic accelerated expansion. The present mechanism for interpreting the nonzero but small cosmological constant provides a new insight into the cosmological constant problem.

On the notion of gauge symmetries of generic Lagrangian field theory

General Lagrangian theory of even and odd fields on an arbitrary smooth manifold is considered. Its nontrivial reducible gauge symmetries and their algebra are defined in this very general setting by means of the inverse second Noether theorem. In contrast with gauge symmetries, nontrivial Noether and higher-stage Noether identities of Lagrangian theory can be intrinsically defined by constructing the exact Koszul–Tate complex. The inverse second Noether theorem that we prove associates with this complex the cochain sequence with the ascent operator whose components define nontrivial gauge and higher-stage gauge symmetries. These gauge symmetries are said to be algebraically closed if the ascent operator can be extended to a nilpotent operator. The necessary conditions for this extension are stated. The characteristic examples of Yang–Mills supergauge theory, topological Chern–Simons theory, gauge gravitation theory, and topological background field (BF) theory are presented.

Reissner—Nordström-de—Sitter-type Solution by a Gauge Theory of Gravity

We use the theory based on a gravitational gauge group (Wu's model) to obtain a spherical symmetric solution of the Geld equations for the gravitational potential on a Minkowski spacetime. The gauge group, the gauge covariant derivative, the strength tensor of the gauge Held, the gauge invariant Lagrangean with the cosmological constant, the Geld equations of the gauge potentials with a gravitational energy-momentum tensor as well as with a tensor of the Geld of a point like source are determined. Finally, a Reissner-Nordstrom-de Sitter-type metric on the gauge group space is obtained.

Some considerations on the Mac Dowell-Mansouri action

A precise relation is established between the Stelle-West formulation of the Mac Dowell-Mansouri approach to a gauge theory of gravity and the approach based on a gauged Wess-Zumino-Witten term. In particular, it is shown that a consistent truncation of the latter correspond to the former. A brief review of the Lovelock-Chern-Simons motivation behind the gauged WZW ones is also done.

Spin-Spin Interactions in Gauge Theory of Gravity, Violation of Weak Equivalence Principle and New Classical Test of General Relativity

For a long time, it has been generally believed that spin-spin interactions can only exist in a theory where Lorentz symmetry is gauged, and a theory with spin-spin interactions is not perturbatively renormalizable. But this is not true. By studying the motion of a spinning particle in gravitational field, it is found that there exist spin-spin interactions in gauge theory of gravity. Its mechanism is that a spinning particle will generate gravitomagnetic field in space-time, and this gravitomagnetic field will interact with the spin of another particle, which will cause spin-spin interactions. So, spin-spin interactions are transmitted by gravitational field. The form of spin-spin interactions in post Newtonian approximations is deduced. This result can also be deduced from the Papapetrou equation. This kind of interaction will not affect the renormalizability of the theory. The spin-spin interactions will violate the weak equivalence principle, and the violation effects are detectable. An experiment is proposed to detect the effects of the violation of the weak equivalence principle.

On Black Holes and Cosmological Constant in Noncommutative Gauge Theory of Gravity

Deformed Reissner-Nordstrom, as well as Reissner-Nordstrom de Sitter, solutions are obtained in a noncommutative gauge theory of gravitation. The gauge potentials (tetrad fields) and the components of deformed metric are calculated to second order in the noncommutativity parameter. The solutions reduce to the deformed Schwarzschild ones when the electric charge of the gravitational source and the cosmological constant vanish. Corrections to the thermodynamical quantities of the corresponding black holes and to the radii of different horizons have been determined. All the independent invariants, such as the Ricci scalar and the so-called Kretschmann scalar, have the same singularity structure as the ones of the usual undeformed case and no smearing of singularities occurs. The possibility of such a smearing is discussed. In the noncommutative case we have a local disturbance of the geometry around the source, although asymptotically at large distances the geometry becomes flat.

A Further Generalized Lagrangian Density and its Special Cases

By summarizing and extending the Lagrangian densities of general relativity and the Kibble’s gauge theory of gravitation,a further generalized Lagrangian density for a gravitational system is obtained and analyzed in greater detail, which will extend the studying range for the theory of gravitation. Many special cases can be derived from this generalized Lagrangian density, and the general characteristics and some peculiarities of them will be described and discussed.

THE ROLE OF TRANSLATIONAL INVARIANCE IN NONLINEAR GAUGE THEORIES OF GRAVITY

The internal structure of the tetrads in a Poincaré nonlinear gauge theory of gravity is considered. Minkowskian coordinates becomes dynamical degrees of freedom playing the role of Goldstone bosons of the translations. A critical length allowing a covariant expansion similar to the weak field approach is deduced, the zeroth order metric being maximally symmetric (Minkowskian in some cases).

Corrections to Schwarzschild solution in noncommutative gauge theory of gravity

A deformed Schwarzschild solution in noncommutative gauge theory of gravitation is obtained. The gauge potentials (tetrad fields) are determined up to the second order in the noncommutativity parameters Θμν. A deformed real metric is defined and its components are obtained. The noncommutativity correction to the red shift test of general relativity is calculated and it is concluded that the correction is too small to have observable effects. Implications of such a deformed Schwarzschild metric are also mentioned.

Yang-Mills Gravity and Gravitational Radiation

A new translation gauge theory of gravity in flat space-time with a new Yang-Mills action involves quadratic gauge curvature and fermions. The theory shows that the presence of an “effective Riemannian metric tensor” for the motions of classical particles and light rays is probably the manifestation of the translation gauge symmetry in flat physical space-time. In the post-Newtonian approximation of the tensor gauge field produced by the energymomentum tensor, the results are shown to be consistent with classical tests of gravity and with the quadrupole radiations of binary pulsars.

Regular accelerating universe without dark energy in Poincaré gauge theory of gravity

Homogeneous isotropic cosmological models with two torsion functions filled with scalar fields and usual gravitating matter are built and investigated in the framework of the Poincaré gauge theory of gravity. It is shown that by certain restrictions on indefinite parameters of gravitational Lagrangian the cosmological equations at asymptotics contain an effective cosmological constant that can explain observable acceleration of cosmological expansion. The behavior of inflationary cosmological solutions at extremely high energy densities is analyzed and regular bouncing solutions are obtained. The role of the spacetime torsion provoking the acceleration of cosmological expansion is discussed.

Coupling Between Spin and Gravitational Field andEquation of Motion of Spin

In general relativity, the equation of motion of the spinis given by the equation of parallel transport, which is a resultof the space-time geometry. Any result of the space-time geometrycannot be directly applied to gauge theory of gravity. In gaugetheory of gravity, based on the viewpoint of the coupling betweenthe spin and gravitational field, an equation of motion of thespin is deduced. In the post Newtonian approximation, it isproved that this equation gives the same result as that of theequation of parallel transport. So, in the post Newtonianapproximation, gauge theory of gravity gives out the same predictionon the precession of orbiting gyroscope as that of general relativity.

DYNAMIC SCALAR TORSION AND AN OSCILLATING UNIVERSE

For the Poincaré gauge theory of gravity we consider the dynamical scalar torsion mode in a cosmological context. We explore in particular the possibility of using dynamical torsion to explain the current state of the accelerating Universe. With certain suitable sets of chosen parameters, this model can give a (qualitatively) proper description of the current universe without a cosmological constant, and the universe described is oscillating with a period of the Hubble time.

Yang–Mills gravity in biconformal space

We write a gravity theory with Yang–Mills-type action using the biconformal gauging of the conformal group. We show that the resulting biconformal Yang–Mills gravity theories describe 4-dim, scale-invariant general relativity in the case of slowly changing fields. In addition, we systematically extend arbitrary 4-dim Yang–Mills theories to biconformal space, providing a new arena for studying flat-space Yang–Mills theories. By applying the biconformal extension to a 4-dim pure Yang–Mills theory with conformal symmetry, we establish a 1-1, onto mapping between a set of gravitational gauge theories and 4-dim, flat-space gauge theories.

EXTENDING THE STUECKELBERG MODEL FOR SPACETIME SYMMETRIES: COSMOLOGICAL IMPLICATIONS

The so-called Stueckelberg transformation is introduced as a prescription of minimal coupling following the procedure of the Utiyama theory, for both internal and spacetime symmetry Lie groups. As a natural example, the theory is applied to the Weyl group and the corresponding gauge gravitational theory is developed. This context appears to be a natural source to account for some sort of dark matter intrinsically related to the gauge-group parameter associated with scale transformations.

YANG–MILLS GRAVITY IN FLAT SPACE–TIME I: CLASSICAL GRAVITY WITH TRANSLATION GAUGE SYMMETRY

We formulate and explore the physical implications of a new translation gauge theory of gravity in flat space–time with a new Yang–Mills action, which involves quadratic gauge curvature and fermions. The theory shows that the presence of an "effective Riemann metric tensor" for the motions of classical particles and light rays is probably the manifestation of the translation gauge symmetry in flat physical space–time. In the post-Newtonian approximation of the tensor gauge field produced by the energy–momentum tensor, the results are shown to be consistent with classical tests of gravity and with the quadrupole radiations of binary pulsars.

Analysis of inflationary cosmological models in gauge theories of gravitation

Inflationary homogeneous isotropic cosmological models filled by scalar fields and ultrarelativistic matter are examined in the framework of gauge theories of gravitation. By using a quadratic scalar field potential, a numerical analysis of flat, open and closed models is carried out. Properties of cosmological models are investigated in dependence on an indefinite parameter of cosmological equations and initial conditions at a bounce. A fulfilled analysis demonstrates the regular character of all cosmological models.